Volume 33, Issue 2
Partial Regularity Result of Superquadratic Elliptic Systems with Dini Continuous Coefficients

Yalin Qiu

Ann. Appl. Math., 33 (2017), pp. 162-185.

Published online: 2022-06

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  • Abstract

We consider the partial regularity for weak solutions to superquadratic elliptic systems with controllable growth condition, under the assumption of Dini continuous coefficients. The proof relies upon an iteration scheme of a decay estimate for a new type of excess functional. To establish the decay estimate, we use the technique of $\mathcal{A}$-harmonic approximation and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, the proof yields directly the optimal Hölder exponent for the derivative of the weak solutions on the regular set.

  • AMS Subject Headings

35J48

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COPYRIGHT: © Global Science Press

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@Article{AAM-33-162, author = {Qiu , Yalin}, title = {Partial Regularity Result of Superquadratic Elliptic Systems with Dini Continuous Coefficients}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {33}, number = {2}, pages = {162--185}, abstract = {

We consider the partial regularity for weak solutions to superquadratic elliptic systems with controllable growth condition, under the assumption of Dini continuous coefficients. The proof relies upon an iteration scheme of a decay estimate for a new type of excess functional. To establish the decay estimate, we use the technique of $\mathcal{A}$-harmonic approximation and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, the proof yields directly the optimal Hölder exponent for the derivative of the weak solutions on the regular set.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20603.html} }
TY - JOUR T1 - Partial Regularity Result of Superquadratic Elliptic Systems with Dini Continuous Coefficients AU - Qiu , Yalin JO - Annals of Applied Mathematics VL - 2 SP - 162 EP - 185 PY - 2022 DA - 2022/06 SN - 33 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/20603.html KW - superquadratic elliptic systems, controllable growth condition, $\mathcal{A}$-harmonic approximation, optimal partial regularity. AB -

We consider the partial regularity for weak solutions to superquadratic elliptic systems with controllable growth condition, under the assumption of Dini continuous coefficients. The proof relies upon an iteration scheme of a decay estimate for a new type of excess functional. To establish the decay estimate, we use the technique of $\mathcal{A}$-harmonic approximation and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, the proof yields directly the optimal Hölder exponent for the derivative of the weak solutions on the regular set.

Qiu , Yalin. (2022). Partial Regularity Result of Superquadratic Elliptic Systems with Dini Continuous Coefficients. Annals of Applied Mathematics. 33 (2). 162-185. doi:
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